Cross-correlation functions are widely accepted as a method for extracting signals from noise, and for establishing the relative timing between two different signals containing a common element. In geolocation applications, a series of samples representing a signal can be acquired from at least two different spatial locations. These samples can then be correlated against each other to determine time difference of arrival (TDOA) between each pairing of signals as observed at each location. Many techniques exist for extracting the TDOA from a cross-correlation, such as determining the time offset for which the cross-correlation function produces a peak amplitude. Other more advanced techniques have been developed to improve the TDOA estimate from the correlation data in the presence of distortion due to multi-path conditions. The goal of all of these techniques is to produce a single number representing the time shift, or TDOA between two signals. This numerical result, when combined with TDOA results from other pairings of receivers, can then be used to estimate the position of the signal source relative to the receivers. Many techniques exist for estimating position using estimated TDOAs.
Techniques that rely on improving the TDOA estimate, or the subsequent solution of location from the TDOA results, can produce poor or misleading estimates of location under multi-path conditions or when more than one signal is present. Moreover, in many instances, signals are not well behaved. That is they are of an unknown origin and can create interference. For RF signals, for example, an unknown emitter may create interference in a cellular network. Other unknown signals may represent a security threat or criminal activity. Frequent observations of these signals may not be possible, as the signals and the environment under which the signals exist may not be well understood and multiple signals may be present at the same time. In cross-correlation plots, multiple signals can result in multiple cross-correlation peaks, which may not be easily distinguishable from multi-path conditions.